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FXYxy

FXYxy is a notational construct used in theoretical computer science and mathematics to denote a class of higher-order binary operators. In its generic form, F, X, and Y stand for operators, while the suffix xy indicates a particular input ordering or paired arguments. The notation is employed mainly in didactic contexts to illustrate how different composition patterns can be encoded compactly.

Definition and usage: For a given F, X, and Y, the expression FXYxy applied to two arguments

Variants and interpretation: Depending on the chosen meaning of F, X, and Y, FXYxy can represent a

Applications and reception: The notation appears in theoretical discussions and educational materials as a compact tool

See also: Function composition, currying, higher-order functions, combinatory logic, lambda calculus.

a
and
b
is
commonly
interpreted
as
F(X(a),
Y(b)).
Variations
exist
where
X
and
Y
may
themselves
be
higher-order
functions,
enabling
nested
application
and
more
complex
argument
binding.
The
lowercase
xy
serves
as
a
cue
for
the
intended
placement
of
a
and
b
within
the
resulting
expression,
helping
to
distinguish
distinct
composition
schemas.
range
of
patterns,
such
as
combining
two
results,
applying
one
operation
to
the
result
of
another,
or
mapping
a
pair
of
inputs
through
a
two-stage
process.
In
teaching
contexts,
FXYxy
is
used
to
compare
and
contrast
function
composition,
currying,
and
the
relationship
between
lambda
calculus
and
combinatory
logic.
for
modeling
structured
function
application.
It
is
not
tied
to
a
single
formal
system
but
rather
to
a
family
of
patterns
that
aid
in
analyzing
how
complex
operations
arise
from
simpler
components.